document.write( "Question 139941: 1. Approximate $\"sqrt%2831%29\"$ by giving the two whole numbers that it lies between \n" ); document.write( "

Algebra.Com's Answer #102000 by jim_thompson5910(35256) $\"\"$ $\"About$

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First, note that the numbers 25 and 36 are perfect squares. In other words, $\"5%5E2=25\"$ and $\"6%5E2=36\"$ . So since 31 is in between 25 and 36, this means that the square root of 31 is in between 5 and 6. In other words, since $\"25%3C31%3C36\"$ , this means $\"5%3Csqrt%2831%29%3C6\"$ . \r
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\n" ); document.write( "\n" ); document.write( "Notice how 31 is 6 units away from 25 and 5 units away from 36. So 31 is about the halfway point from 25 to 36. So a good approximation for $\"sqrt%2831%29\"$ is 5.5 since 5.5 is halfway between 5 and 6.\r
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\n" ); document.write( "\n" ); document.write( "If we take the square root of 31 with a calculator, we get $\"sqrt%2831%29=5.5677643628\"$ . So this shows us that our approximation is very close. \n" ); document.write( "

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